Week of 9/4

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(when is it ok to assume physical expressions are comples?)
(when is it ok to assume physical expressions are complex?)
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So we would write
 
So we would write
  
<math>x = x_r + i x_i , F = F_r + i F_i</math>
+
<math>x = x_r + i x_i F = F_r + i F_i ,</math>

Revision as of 03:04, 8 September 2006

Try the following notebook

Mathematica.png Download manipulating complex numbers in Mathematica.

Also, take a look at Mathematica Tips and Tricks.

A real amplitude and phase measurement. Top figure shows the amplitude of the transmitted and reflected electric fields. Bottom are the corresponding amplitudes.

Emfields.gif


when is it ok to assume physical expressions are complex?

Consider the forced, damped, simple harmonic oscillator.

\ddot{x} + \gamma \dot{x} + \omega_0 ^2 = F/m

Let's pretend that both x and F are actually complex variables. So we would write

x = xr + ixiF = Fr + iFi,

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